System and method for high-temporal resolution, time-resolved cone beam CT angiography

ABSTRACT

A system and method for reconstructing an image using a cone-beam computed tomography (CT) imaging system includes acquiring data from a subject with the CT imaging system using a limited scan range that is less than 360 degrees. The process also includes reconstructing at least one image of the subject having a first temporal resolution from the data acquired, performing a temporal deconvolution of the at least one image using a finite temporal window to generate at least one image of the subject with a second temporal resolution that is greater than the first temporal resolution, and subtracting the at least one image of the subject with the second temporal resolution and a mask image of the subject to generate a time-resolved CT angiogram of the subject.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with government support under EB021183 awardedby the National Institutes of Health. The government has certain rightsin the invention.

BACKGROUND

The present disclosure relates to systems and methods for medical imagereconstruction. More particularly, systems and method are provided forgenerating high-temporal resolution, time-resolved cone beam computedtomography (CT) angiographic images.

Image-based guidance of therapeutic devices, such as catheters, and/orthe placement of interventional devices, such as guidewires and stentsis a key component of modern medicine. Currently, x-ray digitalsubtraction angiography (DSA) and x-ray fluoroscopy are the goldstandard for such image-guided procedures. For example, the tips ofguidewires can be easily visualized using conventional x-ray fluoroscopyby applying small, radio-opaque markers to the tips. As another example,DSA helps visualize and locate the vascular abnormalities and plays acritically important role in diagnosis and treatment planning processes.

Of course, both DSA and x-ray fluoroscopy have substantial limitations,such as its inability to resolve in three dimensions or select specifictwo-dimensional slices. As such, it is common for the clinical workflowto include imaging acquisitions with computed tomography (CT) systems orother multi-dimensional anatomical imaging systems before interventionalmedical procedures or, in some cases, even during an interventionalmedical procedure. Unfortunately, such multi-dimensional orhigh-temporal or spatial resolution anatomical imaging systems aregenerally located in dedicated imaging rooms or facilitates, due to thesize and operational complexity of such systems. As a result, in somecases, it can be necessary to move patients, even repeatedly, fromexamination rooms, to imaging rooms, to operating rooms, andtherebetween to perform successful patient care. Even in specializedsettings where the desired imaging systems may be integrated into anoperating room or other facility, the patient care, which may include aninterventional procedure, must often be interrupted to perform theimaging process, for example, to locate the region of the patent underconsideration within the imaging gantry of a CT system. Unfortunately,this disjointed workflow can be required with patients that areill-equipped to endure the repeated moves between rooms or the delayscaused by the moves, for example, in trauma patients or patients withcardiac or cardiovascular failures.

As such, it would be desirable to have systems and methods that couldprovide clinical caregivers with the desired imaging data, withoutrequiring repeated moves, delays, or general interference with patientcare. Thus, some of the newer generation x-ray angiographic systemsoffers the CT-like data acquisition and reconstruction in the x-rayangiographic suite where the medical treatment procedure takes place.

X-ray projection images encode the variations of the x-ray attenuationproperties of an image object into the transmitted x-ray photons toproduce the shadow image of the object. However, tissues may besuperimposed in the projection image, degrading the diagnosticperformance. When the specific anatomy such as vascular structuresbecome the focus of the clinical task, a variety of subtractiontechniques can be introduced to remove the overlapping structures thatare not relevant to the clinical task from the projection image. In theapplications of contrast enhanced angiography, two images, one withcontrast enhancement (filled) and one without (mask), can be subtractedto generate angiograms to bring the targeted vasculature into the focusof clinical diagnosis. Although the idea of the temporal subtraction oftwo images is not new in modern digital imaging, it was DSA that firstprovided the clinically needed image quality to revolutionize the modernimage-guided interventional procedures. Currently, DSA is anindispensable imaging tool in angiographic suites and the currentclinical gold standard for the diagnosis and image-guided interventionsof vascular abnormalities, including occlusions, stenoses, aneurysms,and so forth.

Although anatomical superposition has been greatly alleviated in twodimensional DSA (2D-DSA), the intrinsically three-dimensional (3D)complex vascular structures may still superpose in 2D-DSA images. Thusthe acquisition of multiple DSA images from several gantry angles isoften needed to provide physicians adequate 3D visualization andunderstanding of complex vasculature. The desire to remove thestructural overlaps in 2D-DSA motivated the idea and experimentalimplementation of 3D-DSA via tomographic reconstruction, which wereinitially acquired using image intensifiers and are currently acquiredusing digital flat-panel detectors. Note that 3D-DSA has also beenreferred to as 3D rotational angiography in literature. In clinicalpractice, the introduction of 3D-DSA in interventional suite has beenfound to have great value in diagnosis and in providing image-guidanceto the treatment of vascular diseases with improved sensitivity andspecificity.

However, a general feature of these so-called C-arm cone beam CT dataacquisition systems is slow in data acquisition due to the safetyconcerns of open gantry C-arm data acquisition platforms. As a result,such systems intrinsically lack dynamic information provided by thecurrent 3D-DSA images acquired from these C-arm cone beam CT dataacquisition systems.

SUMMARY

The present disclosure overcomes the aforementioned drawbacks byproviding systems and methods for reconstructing high temporalresolution time-resolved cone-beam CT angiographic images using acone-beam CT imaging system. As will be described, a “SMART RECON”process is used to reconstructed data acquired from a subject with thecone beam CT imaging system using a limited scan range that is less than360 degrees to create multiple images at a first temporal resolution. Atemporal deconvolution is performed using the generated multiple imageswith a finite temporal window to generate multiple images of the subjectwith a second temporal resolution that is greater than the firsttemporal resolution. A subtraction is performed between the multiplereconstructed images of the subject with the second temporal resolutionand a mask image of the subject to generate a time-resolved CT angiogramof the subject at the second temporal resolution.

In accordance with one aspect of the disclosure, a method is providedfor reconstructing an image using a cone beam computed tomography (CT)imaging system. The steps of the method include a) acquiring data from asubject with the CT imaging system using a limited scan range that isless than 360 degrees, b) initializing an image matrix having columnsthat each correspond to a different image and c) reconstructing at leastone image of the subject having a first temporal resolution from thedata acquired in step a). The reconstructing is performed by i)minimizing a matrix rank of the image matrix, ii) constraining the rankminimization of step c)i) subject to a consistency condition thatpromotes a forward projection of each column in the image matrix to beconsistent with a different subset of the acquired data, each subset ofthe acquired data containing data that are consistent with each otherwhile being inconsistent with data in other subsets of the acquireddata. The method further includes d) performing a temporal deconvolutionof the at least one image using a finite temporal window to generate atleast one image of the subject with a second temporal resolution that isgreater than the first temporal resolution and e) subtracting the atleast one image of the subject with the second temporal resolution and amask image of the subject to generate a time-resolved CT angiogram ofthe subject.

In accordance with another aspect of the disclosure, a method isprovided for reconstructing an image using a cone beam computedtomography (CT) imaging system. The steps of the method include a)acquiring data from a subject with the CT imaging system, the acquireddata acquired using a short scan of less than 360 degrees and containinga plurality of data consistency classes and b) reconstructing an imageof the subject from the data acquired in step a), the image of thesubject containing artifacts associated with the data inconsistencies.The method further includes c) forming an image matrix having a firstcolumn corresponding to the image reconstructed in step b), d) computinga target image matrix by iteratively updating the image matrix formed instep c) by minimizing a matrix rank of the image matrix subject to adata consistency condition such that each column of the computed targetimage matrix corresponds to a different one of the plurality of dataconsistency classes and e) providing each column of the target imagematrix computed in step d) as an image of the subject that issubstantially free of artifacts to produce a series of images of thesubject at a first temporal resolution. The method further includes f)deconvolving the series of images of the subject at the first temporalresolution using a finite temporal window to generate a series of imagesof the subject with second temporal resolution that is higher than thefirst temporal resolution and g) subtracting the series of images of thesubject with the second temporal resolution and from mask images of thesubject to generate a time-resolved CT angiogram of the subject.

In accordance with yet another aspect of the disclosure, a cone beamcomputed tomography (CT) system is provided that includes an x-raysource and associated detectors configured to acquire imaging data froma subject over a range of view angles. The CT system also includes acomputer system including a processor configured to a) control operationof the x-ray source and associated detectors to acquire data from asubject with the CT imaging system using a limited scan range that isless than 360 degrees, b) initialize an image matrix having columns thateach correspond to a different image, and c) reconstruct at least oneimage of the subject having a first temporal resolution from the dataacquired in step a). This reconstruction is performed by i) minimizing amatrix rank of the image matrix and ii) constraining the rankminimization of step c)i) subject to a consistency condition thatpromotes a forward projection of each column in the image matrix to beconsistent with a different subset of the acquired data, each subset ofthe acquired data containing data that are consistent with each otherwhile being inconsistent with data in other subsets of the acquireddata. The processor is further configured to d) perform a temporaldeconvolution of the at least one image using a finite temporal windowto generate at least one image of the subject with a second temporalresolution that is greater than the first temporal resolution and e)subtract the at least one image of the subject with the second temporalresolution and a mask image of the subject to generate a time-resolvedCT angiogram of the subject.

The foregoing and other aspects and advantages of the invention willappear from the following description. In the description, reference ismade to the accompanying drawings which form a part hereof, and in whichthere is shown by way of illustration a preferred embodiment of theinvention. Such embodiment does not necessarily represent the full scopeof the invention, however, and reference is made therefore to the claimsand herein for interpreting the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. is a schematic diagram of a C-arm x-ray computed tomography (CT)imaging system configured in accordance with the present disclosure.

FIG. 2 is a perspective view of an example of an x-ray computedtomography (CT) system.

FIG. 3 is an illustration of an example of a rank-minimized image matrixhaving columns associated with a target image of a subject and anartifact image.

FIG. 4 is an illustration of an example of a rank-minimized image matrixhaving columns associated with a target image of a subject and multipledifferent artifact images.

FIG. 5 is an illustration of an example of a rank-minimized image matrixhaving columns associated with a target image of a subject, an imageassociated with fast motion occurring within the subject during dataacquisition, and an image associated with slower motion occurring withinthe subject during data acquisition.

FIG. 6 is an illustration of an example of a rank-minimized image matrixhaving columns associated with different time frames obtained during adynamic imaging acquisition, each of the different time framescorresponding to a different set of self-consistent data;

FIG. 7 is a flowchart of an example of a method for producing an imageof a subject from data acquired using a CT imaging system in accordancewith the present disclosure.

FIG. 8 is a graph illustrating one example for using a sliding temporalwindow to create segments for using in a reconstruction process inaccordance with the present disclosure.

DETAILED DESCRIPTION

Referring to FIG. 1, an example of a so-called “C-arm” x-ray imagingsystem 100 is illustrated for use in accordance with some aspects of thepresent disclosure. Such an imaging system is generally designed for usein connection with interventional procedures. Such systems stand incontrast to, for example, traditional computed tomography (CT) systems200, such as illustrated in FIG. 2. That is, the traditional CT systemincludes a gantry 202 that forms a bore 204 extending therethrough. Inparticular, the gantry 202 has an x-ray source 206 mounted thereon thatprojects a fan-beam, or cone-beam, of x-rays toward a detector array 208mounted on the opposite side of the bore 204 through the gantry 202.Thus, when a subject 210 is arranged in the bore 204 for imaging usingthe source 206 and detector array 208, access to the subject 210 isrestricted by the gantry 202.

Referring again to FIG. 1, the C-arm x-ray imaging system 100 includes agantry 102 having a C-arm to which an x-ray source assembly 104 iscoupled on one end and an x-ray detector array assembly 106 is coupledat its other end. The gantry 102 enables the x-ray source assembly 104and detector array assembly 106 to be oriented in different positionsand angles around a subject 108, such as a medical patient or an objectundergoing examination, which is positioned on a table 110. When thesubject 108 is a medical patient, this configuration enables a physicianaccess to the subject 108.

The x-ray source assembly 104 includes at least one x-ray source thatprojects an x-ray beam, which may be a fan-beam or cone-beam of x-rays,towards the x-ray detector array assembly 106 on the opposite side ofthe gantry 102. The x-ray detector array assembly 106 includes at leastone x-ray detector, which may include a number of x-ray detectorelements. Examples of x-ray detectors that may be included in the x-raydetector array assembly 106 include flat panel detectors, such asso-called “small flat panel” detectors. Such a detector panel allows thecoverage of a field-of-view of approximately twelve centimeters.

Together, the x-ray detector elements in the one or more x-ray detectorshoused in the x-ray detector array assembly 106 sense the projectedx-rays that pass through a subject 108. Each x-ray detector elementproduces an electrical signal that may represent the intensity of animpinging x-ray beam and, thus, the attenuation of the x-ray beam as itpasses through the subject 108. In some configurations, each x-raydetector element is capable of counting the number of x-ray photons thatimpinge upon the detector. During a scan to acquire x-ray projectiondata, the gantry 102 and the components mounted thereon rotate about anisocenter of the C-arm x-ray imaging system 100.

The gantry 102 includes a support base 112. A support arm 114 isrotatably fastened to the support base 112 for rotation about ahorizontal pivot axis 116. The pivot axis 116 is aligned with thecenterline of the table 110 and the support arm 114 extends radiallyoutward from the pivot axis 116 to support a C-arm drive assembly 118 onits outer end. The C-arm gantry 102 is slidably fastened to the driveassembly 118 and is coupled to a drive motor (not shown) that slides theC-arm gantry 102 to revolve it about a C-axis, as indicated by arrows120. The pivot axis 116 and C-axis are orthogonal and intersect eachother at the isocenter of the C-arm x-ray imaging system 100, which isindicated by the black circle and is located above the table 110.

The x-ray source assembly 104 and x-ray detector array assembly 106extend radially inward to the pivot axis 116 such that the center ray ofthis x-ray beam passes through the system isocenter. The center ray ofthe x-ray beam can thus be rotated about the system isocenter aroundeither the pivot axis 116, the C-axis, or both during the acquisition ofx-ray attenuation data from a subject 108 placed on the table 110.During a scan, the x-ray source and detector array are rotated about thesystem isocenter to acquire x-ray attenuation projection data fromdifferent angles. By way of example, the detector array is able toacquire thirty projections, or views, per second.

The C-arm x-ray imaging system 100 also includes an operator workstation122, which typically includes a display 124; one or more input devices126, such as a keyboard and mouse; and a computer processor 128. Thecomputer processor 128 may include a commercially available programmablemachine running a commercially available operating system. The operatorworkstation 122 provides the operator interface that enables scanningcontrol parameters to be entered into the C-arm x-ray imaging system100. In general, the operator workstation 122 is in communication with adata store server 130 and an image reconstruction system 132. By way ofexample, the operator workstation 122, data store sever 130, and imagereconstruction system 132 may be connected via a communication system134, which may include any suitable network connection, whether wired,wireless, or a combination of both. As an example, the communicationsystem 134 may include both proprietary or dedicated networks, as wellas open networks, such as the internet.

The operator workstation 122 is also in communication with a controlsystem 136 that controls operation of the C-arm x-ray imaging system100. The control system 136 generally includes a C-axis controller 138,a pivot axis controller 140, an x-ray controller 142, a data acquisitionsystem (“DAS”) 144, and a table controller 146. The x-ray controller 142provides power and timing signals to the x-ray source assembly 104, andthe table controller 146 is operable to move the table 110 to differentpositions and orientations within the C-arm x-ray imaging system 100.

The rotation of the gantry 102 to which the x-ray source assembly 104and the x-ray detector array assembly 106 are coupled is controlled bythe C-axis controller 138 and the pivot axis controller 140, whichrespectively control the rotation of the gantry 102 about the C-axis andthe pivot axis 116. In response to motion commands from the operatorworkstation 122, the C-axis controller 138 and the pivot axis controller140 provide power to motors in the C-arm x-ray imaging system 100 thatproduce the rotations about the C-axis and the pivot axis 116,respectively. For example, a program executed by the operatorworkstation 122 generates motion commands to the C-axis controller 138and pivot axis controller 140 to move the gantry 102, and thereby thex-ray source assembly 104 and x-ray detector array assembly 106, in aprescribed scan path.

The DAS 144 samples data from the one or more x-ray detectors in thex-ray detector array assembly 106 and converts the data to digitalsignals for subsequent processing. For instance, digitized x-ray data iscommunicated from the DAS 144 to the data store server 130. The imagereconstruction system 132 then retrieves the x-ray data from the datastore server 130 and reconstructs an image therefrom. The imagereconstruction system 130 may include a commercially available computerprocessor, or may be a highly parallel computer architecture, such as asystem that includes multiple-core processors and massively parallel,high-density computing devices. Optionally, image reconstruction canalso be performed on the processor 128 in the operator workstation 122.Reconstructed images can then be communicated back to the data storeserver 130 for storage or to the operator workstation 122 to bedisplayed to the operator or clinician.

The C-arm x-ray imaging system 100 may also include one or morenetworked workstations 148. By way of example, a networked workstation148 may include a display 150; one or more input devices 152, such as akeyboard and mouse; and a processor 154. The networked workstation 148may be located within the same facility as the operator workstation 122,or in a different facility, such as a different healthcare institutionor clinic.

The networked workstation 148, whether within the same facility or in adifferent facility as the operator workstation 122, may gain remoteaccess to the data store server 130, the image reconstruction system132, or both via the communication system 134. Accordingly, multiplenetworked workstations 148 may have access to the data store server 130,the image reconstruction system 132, or both. In this manner, x-raydata, reconstructed images, or other data may be exchanged between thedata store server 130, the image reconstruction system 132, and thenetworked workstations 148, such that the data or images may be remotelyprocessed by the networked workstation 148. This data may be exchangedin any suitable format, such as in accordance with the transmissioncontrol protocol (“TCP”), the Internet protocol (“IP”), or other knownor suitable protocols.

With conventional image reconstruction techniques, such as filteredbackprojection for CT/C-arm CT imaging and Fourier-based reconstructionstechniques for magnetic resonance imaging (MRI), a single image isreconstructed from a corresponding set of data acquired with the medicalimaging system. For example, one image is reconstructed from a singlesinogram in x-ray CT/C-arm CT imaging and one image is reconstructedfrom one k-space data set in MRI. This correspondence between data andthe images reconstructed from that data is a function of traditionalimage reconstruction techniques and the fact that such techniques arebased on an assumption that all of the acquired data are consistent witheach other. Routinely, however, data acquired with medical imagingsystems are not consistent with a single true image of the subject beingimaged, or a single state of a true image object that has dynamiccharacteristics.

These inconsistencies manifest as artifacts in the reconstructed imagesand can have many different origins. For example, in x-ray CT/C-arm CTimaging, artifacts can result from the presence of metal objects in thesubject, by acquiring too few projections, from beam-hardening effects,from x-ray scattering, subject motion, and so on. In MRI, artifacts canresult from undersampling k-space, magnetic field inhomogeneities,subject motion, and so on. Inconsistencies between the acquired data andthe stationary state of a true image of the subject can also have othersources, such as the presence of an exogenous contrast agent that ifadministered to the subject and the travels through the subject'svasculature. The assumption that the reconstructed image should beconsistent with the acquired data is embodied in the following imagingmodel:AI=Y  (1);

which states that image reconstruction techniques should seek toreconstruct an image, I, that when forward projected is consistent withthe acquired data, Y. The matrix, A, is referred to as the systemmatrix, which can be generally regarded as a forward projection operatorthat relates the reconstructed image, I, to the acquired data samples,Y. Eqn. (1) imposed that the reconstructed image, I, must be consistentwith the measured data samples, Y; thus, Eqn. (1) can also be referredto as the “data consistency condition.” In x-ray CT imaging, the systemmatrix can include a reprojection operation and in MRI the system matrixcan include a Fourier transform operation. The consistency condition ofEqn. (1), put in other words, states that when an image is faithfullyreconstructed, the forward projection of that image should besubstantially similar to, or consistent with, the data actually acquiredwith the imaging system.

To reconstruct an image, I, from the measured data, Y, it is oftenrequired that the data satisfy the so-called data sufficiency condition,which is a condition that allows for an inverse reconstruction formulato be used to reconstruct the image from the measured data. In x-ray CTimaging, the data sufficiency condition is the so-called Tuy condition,which requires the data samples to be acquired in an extended angularrange around the image object. In MRI, the data sufficiency condition isthe complete population of the entire Fourier space. Even when the datasufficiency condition is satisfied, however, still another conditionneeds to be met to reconstruct a true image of the image object. Thediscretely acquired data samples also need to satisfy the associatedsampling criterion for a given reconstruction scheme.

Examples of data sampling criteria include the view angle samplingrequirement in x-ray CT and the Nyquist sampling criterion in MRI. Whenthe data sampling criterion is met in x-ray CT, filtered backprojectioncan be used to reconstruct an image, and when the data samplingcriterion is met in MRI, Fourier inversion can be used to reconstruct animage. When an iterative image reconstruction method is employed, thedata sampling criteria are often significantly relaxed. One example ofsuch a method is compressed sensing based iterative image reconstructiontechniques.

In an ideal situation, when the aforementioned data sufficiencycondition and data sampling conditions are satisfied, an artifact-freeimage can be reconstructed. This ideal situation is impractical in thereal world, however, due to complications of data acquisition conditionsand complications from the objects being imaged. As a result of thesecomplications, the acquired data may not represent the same physicalstate of the image object, or may not be acquired under the samephysical conditions. Thus, the acquired data are referred to as“inconsistent data.” The physical reasons for these inconsistencies,whether because of a non-ideal acquisition system or because of a changein the physical state of the object during data acquisition, arereferred to as the sources of inconsistency.

When the acquired data are no longer consistent due to sources ofinconsistency, such as those described above, the consistency conditionbegins to break down. That is, the acquired data are no longerconsistent when physical effects such as subject motion, contrastenhancement, noise, beam hardening in x-ray imaging, and so on arepresent during the data acquisition process. The inconsistencies in theacquired data manifest as artifacts in the reconstructed images.

Described here are systems and methods for generating time-resolved CTangiography with selectably high temporal resolution. The system andmethod can leverage a process for simultaneous image artifact reductionand tomographic image reconstruction, which may thus be referred to as a“SMART-RECON.” As will be described, SMART RECON can be applied toreconstruct multiple cone-beam CT images from a single-pass cone beam CTdata set. The systems and methods are advantageously suited for medicalimaging applications, such as time-resolved computed tomography (“CT”),cone-beam CT, cardiac imaging CT, contrast-enhanced CT, and x-rayangiography, and, particularly, provides the ability to simplify the waytime-resolved images for interventional procedures are acquired and easeclinical workflow. The present systems and methods can be used to reduceradiation dose and contrast dose and, as a result, enhance patientsafety, since only IV contrast injection is needed. The process can beperformed at outpatient clinics.

In general, the image reconstruction operates by minimizing the rank ofa generalized matrix that contains the target image and other imagesthat are associated with acquired data that have different degrees ofconsistency. This method, and several examples of its implementation,are described below in detail.

With conventional image reconstruction techniques, such as filteredbackprojection for x-ray CT imaging and Fourier-based reconstructiontechniques for MRI, one image is reconstructed from one data set,despite the existence of data inconsistencies. For example, one image isreconstructed from a single sinogram in x-ray CT imaging and one imageis reconstructed from one k-space data set in MRI. This correspondencebetween data and the images reconstructed from that data is becausethese traditional image reconstruction techniques are based on theassumption that all of the acquired data are consistent with each otherand satisfy the sufficiency condition. By way of example, data acquiredwith an x-ray CT imaging system lose their consistency when the subjectmoves during data acquisition, when an exogenous contrast agent isadministered to the subject, and when the x-ray beam is no longermonochromatic (e.g., when beam-hardening occurs). Again, this assumptionis embodied in the so-called forward imaging model, or “consistencycondition” of Eqn. (1).

Conventional image reconstruction methods, such as filteredbackprojection for x-ray CT, Fourier inversion for MRI, and iterativereconstruction from all acquired data, there is no intrinsic mechanismthat accounts for the degree of data consistency or inconsistency. Thesingle indication of data inconsistency is the appearance of imageartifacts in the reconstructed image. To reduce the artifact levels, theacquired data can be preprocessed with the appropriate technique for thetype of artifacts present in the image. It is unknown, however, to whatextent the acquired data should be corrected before imagereconstruction.

It is noted that tomographic reconstructions, such as filteredbackprojection, have a certain level of tolerance to datainconsistencies. For example, data inconsistency may not necessarilyresult in image artifacts in the reconstructed image, but the thresholdfor this tolerance to inconsistencies cannot be known a priori. Thus, itremains highly desirable to develop systems and methods that canautomatically account for data inconsistencies during the imagereconstruction process.

The acquired data are no longer consistent when physical effects such assubject motion, contrast enhancement, noise, beam hardening in x-rayimaging, and so on are present during the data acquisition process.These inconsistencies in the acquired data manifest as artifacts in thereconstructed images.

To address this problem, the present disclosure provides systems andmethods for image reconstruction that account for intrinsic dataconsistency in acquired data, which allows for images to be separatelyreconstructed with different artifact levels that depend on theinconsistency level of the acquired data. In many cases, an image withminimal artifacts will be reconstructed from those consistent datasamples, together with an image that primarily depicts artifacts fromother data with higher levels of inconsistency in the acquired data.

This concept can be interpreted as seeking to reconstruct the maximallyavailable generalized image matrix, X, from the acquired data. If theacquired set of data samples has N_(S) data samples, the worst casescenario is that all of the data samples are inconsistent with oneanother. In this case, N_(S) images would be required to delineate thephysical state of the image object. As a result, the maximally availablegeneralized image matrix, X, would have N_(S) columns. The number ofrows in the maximally available generalized image matrix, X, would bethe total number of image pixels for a two-dimensional image, or thetotal number of image voxels for a three-dimensional image volume. Bylowering the rank of this generalized image matrix while constrained bythe data consistency condition of Eqn. (1), the images with differentartifact levels can be reconstructed by automatically groupingconsistent data into a series of images that reflects the consistencylevel among the data.

The connection between data consistency and image matrix rank reductioncan be understood as follows. When the acquired data are all consistent(e.g., from each view angle in x-ray CT imaging or with respect to eachline in k-space in MRI), all columns in the maximally availablegeneralized image matrix, X, will be the same. Mathematically, thisgeneralized image matrix, X, thus has a column rank of one, orRank(X)=1. When the acquired data can be divided into two consistencyclasses in some way, then the rank of the maximally availablegeneralized image matrix, X, will increase to two, or Rank(X)=2. In thisinstance, the rank of the maximally available generalized image matrixcan be reduced to two. In other words, the rank reduced generalizedimage matrix, X, contains only two columns,X=[X ₁ X ₂]  (2);

where each column corresponds to an image reconstructed from the data inthe associated consistency class.

The increase in rank is because the acquired data contains two distinctgroups of data that are each internally consistent, but inconsistentwith each other. An example of this is when data is acquired from asubject who moves during data acquisition. The data acquired when thesubject was not moving will not be consistent with the data acquiredwhen the subject was moving. On the other hand, the data acquired whenthe subject was not moving will be internally consistent, as will thedata acquired when the subject was moving. This property is exploited bythe present disclosure to reconstruct an image that is free of thecontributions from the inconsistent data. As will be described below,there can be more than two consistency classes in the acquired data andeach of these consistency classes can be separated from each other.

In general, an image that is free of the contributions from inconsistentdata can be obtained by minimizing the rank of the maximally availablegeneralized image matrix, X, such that the forward projection of thedesired column of the maximally available generalized image matrix,X_(n)=I_(n), is consistent with the associated consistency class in theacquired data, Y_(n). That is,

$\begin{matrix}{{\arg\;{\min\limits_{X}{\left\{ {{Rank}(X)} \right\}\mspace{14mu}{such}\mspace{14mu}{that}\mspace{14mu}{AI}_{n}}}} = {Y.}} & (3)\end{matrix}$

The rank minimization described by Eqn. (3) automatically anditeratively groups consistent data from different sources into severalirreducible image columns in X. It is noted that the individual image,I_(n), corresponds to a different consistency class and is a columnvector in the generalized image matrix, X. That is,X=[I ₁ . . . I _(N)]  (4).

Here, the individual image, I_(n), corresponding to a particularconsistency class is formed by applying a vectorization operation to anordinary image with two indices,I _(n) =vec(I _(n)(x,y))  (5);

or with three indices,I _(n) =vec(I _(n)(x,y,z))  (6).

Numerically, it is an NP-hard problem to solve the rank minimizationproblem because it is equivalent to solving a zero-norm minimizationproblem. This point can be illustrated by introducing a singular valuedecomposition (“SVD”) operation to the generalized image matrix, X, asfollows:X=UΣV  (7);

where the U and V matrices are orthogonal and the Σ matrix is a diagonalmatrix with r non-zero elements, referred to as the singular values,σ_(i), of the matrix,Σ=diag{σ₁,σ₂, . . . ,σ_(r),0,0, . . . ,0}  (8).

As long as this SVD is performed, the rank of the generalized imagematrix, X, is said to be r. Thus, minimization of the rank of thegeneralized image matrix, X, can be equated to minimizing the followingzero-norm:

$\begin{matrix}{{{\arg\;{\min\limits_{X}\left\{ {{Rank}(X)} \right\}}} \equiv {\arg\;{\min\limits_{X}{X}_{0}}}};} & (9)\end{matrix}$

where ∥X∥₀ is the zero-norm of the generalized image matrix, X, which isequal to the number of non-zero diagonal elements in the singular valuedecomposition of the generalized image matrix, X. The zero-norm problemin Eqn. (9) can be practically relaxed to an l₁-norm, as is often donein compressed sensing. Namely, instead of directly solving the problemin Eqn. (3), the problem is relaxed to the following convex optimizationproblem:

$\begin{matrix}{{\arg\;{\min\limits_{X}{X}_{*}}};} & (10)\end{matrix}$

where ∥X∥_(*) is the so-called nuclear norm of the generalized imagematrix, X, which can be given by,

$\begin{matrix}{{X}_{*} = {{\sum\limits_{i = 1}^{r}{\sigma_{i}}} = {\sum\limits_{i = 1}^{r}{{\sum_{ii}}.}}}} & (11)\end{matrix}$

More generally, the more general Schatten p-norm can be used to relaxthe precise rank minimization in Eqn. (3). The Schatten p-norm isdefined as,

$\begin{matrix}{{X}_{p}^{p} = {\sum\limits_{i}{\sigma_{i}^{p}.}}} & (12)\end{matrix}$

Using the Schatten p-norm, the rank minimization in Eqn. (3) can berelaxed as the following convex optimization problem for p≥1:

$\begin{matrix}{{\arg\;{\min\limits_{X}{{X}_{p}^{p}\mspace{14mu}{such}\mspace{14mu}{that}\mspace{14mu}{AI}_{n}}}} = {Y.}} & (13)\end{matrix}$

The constrained optimization problem in Eqn. (13) can be solved byminimizing the following objective function with a quadratic penalty:

$\begin{matrix}{{\arg\;{\min\limits_{X}\left\{ {{\frac{1}{2}{{{AI}_{n} - Y}}_{D}^{2}} + {\lambda{X}_{p}^{p}}} \right\}}};} & (14)\end{matrix}$

where the weighted norm for a generalized input is given as,∥Z∥ _(D) ² =Z ^(T) D  (15);

with the diagonal matrix, D, given by,

$\begin{matrix}{{D = {{diag}\left\{ {\frac{1}{\xi_{1}^{2}},\frac{1}{\xi_{2}^{2}},\ldots}\mspace{14mu} \right\}}};} & (16)\end{matrix}$

where ξ_(i) ² is the noise variance for the i^(th) measured data sample.Therefore, the diagonal matrix, D, accounts for noise in the measureddata samples by assigning a lower weight to higher noise data and ahigher weight to lower noise data. The parameter, λ, is used to tradeoffthe data fidelity term and the relaxed matrix rank minimization term inEqn, (14). The equivalence of the constrained optimization problem inEqn. (13) and the unconstrained optimization problem in Eqn. (14) can bereached in the limit of λ=∞. Additionally, the constrained optimizationproblem in Eqn. (13) can be solved using the well-known augmentedLagrangian multiplier method.

In Eqn. (14), rank minimization can be viewed as a regularization to thenoise-penalized least square minimization. In addition to the above rankregularization, other additional regularization methods can also beadded to Eqn. (14). One example of additional regularization methodsincludes the prior image constrained compressed sensing (“PICCS”)objective function, which is described in U.S. Pat. Nos. 8,194,937;8,229,199; and 8,374,413, which are each herein incorporated byreference in their entirety. By incorporating the PICCS objectivefunction, Eqn. (14) can be generalized as,

$\begin{matrix}{{\arg\;{\min\limits_{X}\left\{ {{\frac{\lambda}{2}{{{AI}_{n} - Y}}_{D}^{2}} + {X}_{p}^{p} + {\alpha{{\Psi_{1}I_{n}}}_{q}^{q}} + {\left( {1 - \alpha} \right){{\Psi_{2}\left( {I_{n} - I_{P}} \right)}}_{q}^{q}}} \right\}}};} & (17)\end{matrix}$

where Ψ₁ and Ψ₂ are sparsifying transforms, which promote sparsity ineach individual image component, I_(n); I_(P) is a prior image in thePICCS reconstruction; the parameter, α, is used to assign a weight tothe term without the prior image contribution and to the term with theprior image contribution; and the q-norm of a vector, Z, is defined as,

$\begin{matrix}{{Z}_{q}^{q} = {\sum\limits_{j = 1}^{N}{{Z_{j}}^{q}.}}} & (18)\end{matrix}$

When a blind SVD operation is applied to the generalized image matrix,X, it can be computationally expensive. In practice, it is contemplatedthat the target rank of the generalized image matrix will generally below; thus, a truncated SVD decomposition can be used in a numericalimplementation. As one example, the lowest rank approximation can beused, in which Rank(X)=1. In this case, all of the acquired data samplesare used to reconstruct a single image. The conventional numericallyefficient methods for solving such a problem is an image reconstructiontechnique such as filtered backprojection for x-ray CT data or Fourierinversion for k-space data acquired with an MRI system. This first passestimation can be used as the initial guess for the first column of thegeneralized image matrix, X. The rank minimization process can theniteratively proceed to rank two, rank three, an upwards to the desiredrank r solution. In practice, it is contemplated that r≤20 will besufficient for most clinical imaging applications. In this case, theacquired data are sorted into r different consistency classes. Using thefirst column as the prior image, I_(P), the PICCS algorithm can be usedto reconstruct the r columns of the generalized image matrix, X. Havingobtained these initial solutions, the generalized image matrix, X, canbe decomposed into the following form:

$\begin{matrix}\begin{matrix}{X = \begin{bmatrix}I_{1} & I_{2} & \ldots & I_{N - 1} & I_{N}\end{bmatrix}} \\{= {U^{{MN} \times r}{\sum^{r \times r}{V^{r \times {MN}}.}}}}\end{matrix} & (19)\end{matrix}$

Here, the initially estimated r column images fill in the r columns inthe U matrix. One of the optimization problems in Eqns. (3), (10), (13),(14), or (17) can be solved to iteratively determine the diagonalmatrix, Σ, and also the V matrix. Furthermore, if the multiplication ofthe diagonal matrix, Σ, and the V matrix is treated as a single matrix,{tilde over (V)} ^(r×MN) =ΣV  (20);

then the optimization problem in Eqns. (3), (10), (13), (14), or (17)can then be solved iteratively to determine the matrix, {tilde over(V)}.

When the above decomposition of the generalized image matrix, X, isperformed such that the image matrix, X, is decomposed into thefollowing matrix multiplication:X=UV  (21);

sparsity constraints and other regularizations can be directly appliedto the two matrix components, U and V. As a result, the followingvariation in the optimization problem can be provided.

$\begin{matrix}{\arg\;{\min\limits_{X}{\left\{ {{\frac{1}{2}{{{AI}_{n} - Y}}_{D}^{2}} + {\lambda_{1}{{\Psi_{1}U}}_{1}} + {\lambda_{2}{{\Psi_{2}V}}_{1}}} \right\}.}}} & (22)\end{matrix}$

When the above described procedure to compute the U matrix is used, thesecond term in Eqn. (22), λ₁∥Ψ₁U∥, can be set to zero to improvenumerical efficiency.

For instance, in an x-ray CT imaging application, the rank minimizationwill automatically and iteratively group consistent data from differentview angles into several irreducible image columns. The numerical valueof the final rank of the generalized image matrix, X, is the number ofdistinct images that are reconstructed from the acquired data. Each ofthese distinct images corresponds to a different subset of the acquireddata that is internally consistent.

Classification of data consistency classes will depend on the particularimaging application. In an x-ray CT application, data samples acquiredat each given x-ray source position often represents a consistency classwhen dynamic CT imaging is performed. Examples of dynamic CT imagingincludes cardiac CT imaging in diagnostic multislice CT;contrast-enhanced CT imaging, with or without organ motion involved;time-resolved cone-beam CT in image-guided radiation therapy; antime-resolved cone-beam CT using a C-arm based cone-beam CT system inimage-guided interventions.

When multi-energy CT acquisitions are employed, the consistencyclassification will be dependent on the x-ray spectrum. Thus, for dualenergy CT acquisitions, it is natural to classify the data and imagesinto two consistency classed corresponding to the two energy levelsutilized in the imaging procedure.

When a conventional single spectrum CT data acquisition is used, thedata and images can be classified into two or more classes that aredetermined by the x-ray path lengths and image content. When highlyattenuating objects, such as bony structures or exogenous metallicobjects, are present in the subject, the measured data points passingthough these highly attenuating objects and those measured data that donot pass through these highly attenuating objects can be classified intodifferent consistency classes.

For an MRI system that is used to generate dynamic imaging, such ascardiac MRI or time-resolved contrast-enhanced MRI, the data consistencyand corresponding image classes can be sorted based on prior knowledgeof the cardiac and/or respiratory phase.

The higher the rank of the maximally available generalized image matrix,X, the more consistency classes that will be sought in the acquireddata. That is to say, as the rank of the maximally available generalizedimage matrix, X, increases, the inconsistencies in the acquired datawill be spread to more images. Depending on the imaging application,this feature can be advantageously relied upon to separate a generalclass of inconsistency into smaller subsets. For example, motionartifacts can be parsed into motions occurring at different speeds. Inthis manner, slower motion artifacts (e.g., respiratory motion) can beseparated from faster motion artifacts (e.g., cardiac motion).

The rank minimization can also be combined with other minimizationconstraints to further improve image quality. For instance, theminimization presented in Eqn. (3) can be additionally constrainedsubject to conditions or optimization requirements. One example of anadditional constraint is a prior image constrained compressed sensing(“PICCS”) constraint, such as the ones described in U.S. Pat. Nos.8,194,937; 8,229,199; and 8,374,413, which are each herein incorporatedby reference in their entirety. Alternatively, other compressed sensingconstraints could be imposed while minimizing the rank of the maximallyavailable image matrix.

Advantageously, minimizing the rank of the maximally available imagematrix in this manner allows for the separation of unwanted componentsof an image from the desirable components. In some instances, theunwanted components can then be used to further correct the desirablecomponents or to ascertain additional information about the subject.Several applications of this method will now be described.

With reference now to FIG. 3, the above-described SMART RECON method canbe used to produce a rank R=2 maximally available image matrix, X,having two columns corresponding to two consistency classes of theacquired data. The first column contains the target image, in whichsubstantially no image artifacts are present. The second column containsan artifact image that depicts the inconsistencies in the acquired data,which are generally regarded as image artifacts. For instance, thisartifact image can include contributions associated with streakartifacts, aliasing artifacts, scatter artifacts, beam hardeningartifacts, motion artifacts, and so on. As one example, when metalartifacts and beam hardening corrupt CT images, the method of thepresent disclosure is capable of searching for a target image withminimal metal and beam hardening artifacts while also optionallyreturning other images that depict primarily only the respectiveartifacts.

As illustrated in FIG. 4, the above-described SMART RECON method canalso be used to further separate an artifact image into multipledifferent artifact images by selecting the appropriate rank at which toconclude the rank minimization of the maximally available image matrix.For instance, the method of the present disclosure can be used toseparate different artifacts into different images, such as one imagefor streak artifacts and another image for beam-hardening artifacts.This result is attainable because one type of image artifact (e.g.,aliasing) will be inconsistent relative to another type of imageartifact (e.g., beam-hardening). As such, the different artifact typeswill generally belong to different consistency classes that will beseparated by the method of the present disclosure. Separating theartifacts into different artifact images is advantageous wheninformation about the specific artifact sources can provide additionalinformation

As illustrated in FIG. 5, the above-described SMART RECON method canalso be used to separate static and moving portions of an image or timeseries of images. Not only can the static and moving portions beseparated, but the moving portions can be divided into two or moreimages depicting regions of the image field-of-view (“FOV”) that aremoving at different speeds. In this manner, regions of the image FOVthat affected by different motion sources can be separated out. Forinstance, motion associated with respiration can be separated fromcardiac motion or the motion of a tumor. As a result, respiratory orcardiac gating can be achieved without the need for additionalprocessing or motion information acquisition.

As illustrated in FIG. 6, the above-described SMART RECON method is alsocapable of reconstructing a series of image frames, such as a series ofimages depicting a vasculature during a time-resolved angiographic orperfusion imaging procedure, a subject's heart during a cardiac imagingprocedure, a subject's respiration, and so on. In these instances, themethod of the present disclosure is able to recover a set of consistentimages of the subject acquired during the course of data acquisition. Asone example, in cardiac imaging applications, the method can be used toproduce motion consistent images for each cardiac phase because the dataacquired at a given phase of the cardiac cycle will be largelyconsistent with other data acquired at the same cardiac phase, whereasdata acquired at different cardiac phases will be largely inconsistent.The method can also be implemented in contrast-enhanced imagingapplications to generate several consistent time frames from one shortscan data acquisition, which can then be used to provide selectably-hightemporal resolution, time-resolved, CT angiographic images. Such imagesare particularly useful for analyzing the cardiovascular structures,such as when guiding interventional procedures related thereto.

In particular, referring to FIG. 7, a flowchart setting forth the stepsof an example of a method for producing an image in accordance with thepresent disclosure is illustrated. The method begins with theacquisition of data using a medical imaging system, as indicated at step702. The data acquisition can be performed with any suitable medicalimaging system, including an x-ray computed tomography system, an x-raytomosynthesis system, or an x-ray C-arm system, or even a magneticresonance imaging system, an ultrasound system, a positron emissiontomography system, or the like.

In the present example, the acquisition may be performed by using aC-arm system, such as described above with respect to FIG. 1, or othersystem that is suitable for acquiring angiographic images, such as maybe particularly useful for guiding interventional procedures. As will bedescribed, the systems and methods of the present disclosure are capableof combining the images associated with a CT/angio-suite using systemsthat are not typically employed in CT/angio-suites, to provideinformation about soft tissue, angiography, and perfusion. Moreparticularly, the data acquired at step 702 may be acquired using aso-called “short scan.” As described herein, a “short scan” may referto, for example, a CT acquisition that extends over approximately 180degrees, plus the fan angle, which provides an approximate range of 200degrees. However, greater ranges can be used, if desired. Likewise, insome situations it may be desirable to perform a short scan over an evenshorter angular range, including so-called quarter-scans.

Acquiring data at step 702 may include acquiring data with and withoutthe use of a vascular contrast agent. That is, step 702 may both a firstC-arm acquisition with contrast and a time-resolved, cone beamangiographic acquisition to acquire selectively-high spatial andtemporal resolution. Also, acquisitions can be designed to acquire onlyarterial data or only venous data. As one non-limiting example,acquiring data at step 702 may be achieved using approximately 10 sweepsof a C-arm system, such as illustrated in FIG. 1. However, this numberof sweeps can be greatly reduced, such as to only 2 sweeps of the C-armsystem—one with contrast enhancement via a vascular contrast agent, suchas iodine, and one without contrast enhancement.

As a separate example, the scan may be performed over a time period of,as a non-limiting example, approximately 5 seconds to approximately 20seconds. Referring to FIG. 8, a given sweep may be performed over a time“T” that can be divided into segments, in this example, 5 segments,S1-S5. In this way, a contrast curve 800 is divided into 5 sets of viewangles, which, as will be described, may be treated equally duringreconstructing (i.e., no weighting).

After data have been acquired, the image reconstruction processgenerally begins 703. First, an image matrix having column that will beassociated with different images is initialized, as indicated at step704, and as described above. Optionally, a desired rank to which theimage matrix should be minimized is selected, as indicated at step 706.As discussed above, the choice of image matrix rank can be determinedusing a singular value decomposition of the image matrix. As indicatedgenerally at 708, a target image of the subject is then reconstructedusing SMART RECON or an iterative rank minimization process that issubject to a consistency condition constraint in which each column ofthe image matrix is required to be consistent with a unique subset ofthe acquired data that is to some extent inconsistent with the rest ofthe acquired data. That is, each column of the reconstructed imagematrix will correspond to an image representative of a unique subset ofthe acquired data.

As described above, the data acquired at step 702 may be acquired usinga “short scan.” As such, the subsets may be selected based on theangular range of acquisition. Based on angular range, each of thesesubsets of the acquired data contain data that are consistent with eachother, but at the same time, each subset of the acquired data containdata that are generally inconsistent with data not included in thesubset. As such, the image reconstruction process is capable ofautomatically separating the acquired data into different subsets ofdata that each correspond to a unique consistency class. For example, inthe example of FIG. 8, the data acquired at segment S1 is different inboth view angle and contrast from the data acquired at segment S2. Byminimizing the rank of the image matrix, the fewest possible number ofsuch consistency classes is sought. As noted above, however, the desiredimage matrix rank can also be selected to force the separation of theacquired data into a predefined number of consistency classes.

The reconstruction of the image matrix, thus, includes establishing theaforementioned consistency condition between the columns of the imagematrix and subsets of the acquired data, as indicated at step 710. Therank of the image matrix is then minimized, as indicated at step 712.Thus, a SMART RECON reconstruction is performed using finite temporalwindow defined by the angular range used to acquire the data.

This process is iteratively repeated until a stopping criterion is met,as determined at decision block 714. Examples of stopping criterioninclude when a target rank, which may be optionally selected asdescribed above, is achieved, and when the difference of the estimatedvalues in two consecutive iterations is smaller than a predeterminedthreshold value. If the stopping criterion is not met, the nextiteration of the minimization begins, as indicated at step 716.

When the process of creating the initial images of the subject usingSMART RECON 708 is complete, a set of images is provided at step 718with a first, finite temporal window defined by the angular range ofacquisition. At step 720, a temporal deconvolution is then applied tothe reconstructed time-resolved cone beam CT images with the first,finite temporal window width to generate time-resolved cone beam CTimages with a second temporal resolution that is higher than the firsttemporal resolution to provide the a selectivity in temporal resolution.Put another way, the time-resolved cone-beam CT images generated at step720 define a continuous temporal sampling to provide the clinician withan infinitely high temporal resolution. That is, the images generatedusing SMART RECON provide definitive temporal behavior. As describedabove, the data for each segment is unweighted. Thus, the deconvolutionperformed at step 720 determines the true temporal behavior.

At step 722 the images generated in step 720 may be corrected forpotential temporal truncation effects, such as caused by the limiteddata acquisition performed at step 702, such as by using theabove-described short scan or other limited range of view angles. Forexample, this correction for potential temporal truncation may beperformed using a gamma-variate fit that is applied to the imagesgenerated in step 720.

At step 724 a time-resolved angiogram is generated that defines acontinuous temporal sampling. In particular, a time-resolved cone beamCT angiogram with the second, higher temporal resolution is generated byperforming a mask subtraction, for example, using one of the first orlast images acquired.

In some applications, step 724 may complete the process. Optionally, theangiograms generated at process step 724 may be used to create virtual2D digital subtraction angiography (DSA) images. For example, a conebeam forward projection can be applied to the image series generated atstep 724 to generate virtual 2D DSA images from any perspective angle.

As such, systems and methods are provided to simplify the waytime-resolved images for interventional procedures are acquired and easeclinical workflow. The above-described systems and methods reduceradiation dose, contrast dose, and, as a result, enhance patient safetysince only IV contrast injection is needed. The procedure can thus beperformed at outpatient clinics.

The present invention has been described in terms of one or morepreferred embodiments, and it should be appreciated that manyequivalents, alternatives, variations, and modifications, aside fromthose expressly stated, are possible and within the scope of theinvention.

The invention claimed is:
 1. A method for reconstructing an image usinga cone-beam computed tomography (CT) imaging system, the steps of themethod comprising: a) acquiring data from a subject with the CT imagingsystem using a limited scan range that is less than 360 degrees; b)initializing an image matrix having columns that each correspond to adifferent image; c) reconstructing at least one image of the subjecthaving a first temporal resolution from the data acquired in step a) by:i) minimizing a matrix rank of the image matrix; ii) constraining therank minimization of step c)i) subject to a consistency condition thatpromotes a forward projection of each column in the image matrix to beconsistent with a different subset of the acquired data, each subset ofthe acquired data containing data that are consistent with each otherwhile being inconsistent with data in other subsets of the acquireddata; d) performing a temporal deconvolution of the at least one imageusing a finite temporal window to generate at least one image of thesubject with a second temporal resolution that is greater than the firsttemporal resolution; and e) subtracting the at least one image of thesubject with the second temporal resolution and a mask image of thesubject to generate a time-resolved CT angiogram of the subject.
 2. Themethod as recited in claim 1 in which the limited scan range is 200degrees or less, including a fan angle.
 3. The method as recited inclaim 1 in which the CT imaging system generates a cone beam and whereinthe at least one image of the subject with second temporal resolutionincludes time-resolved cone beam CT images with a continuous temporalsampling.
 4. The method as recited in claim 1 further comprisingperforming a gamma-variate fit to the at least one image of the subjectwith the second temporal resolution to correct for potential temporaltruncation effects caused by the limited scan range.
 5. The method asrecited in claim 1 further comprising f) applying a cone-beam forwardprojection to the time-resolved CT angiogram to generate a virtual 2Dangiography image.
 6. The method as recited in claim 1 in which step a)includes an acquisition with intravenous (IV) contrast and withoutcontrast.
 7. The method as recited in claim 1 in which the CT imagingsystem is a C-arm CT imaging system.
 8. The method as recited in claim 1in which the data acquired in step a) includes inconsistencies and stepc) includes reconstructing a target image of the subject that issubstantially free of image artifacts and at least one artifact imagethat contains substantially only image artifacts associated with theinconsistencies.
 9. The method as recited in claim 1 in which the dataacquired in step a) is representative of a time series of images andstep c) includes reconstructing the time series of images, wherein eachcolumn in the image matrix corresponds to one of the images in the timeseries.
 10. A method for reconstructing an image using a cone-beamcomputed tomography (CT) imaging system, the steps of the methodcomprising: a) acquiring data from a subject with the CT imaging system,the acquired data acquired using a short scan of less than 360 degreesand containing a plurality of data consistency classes; b)reconstructing an image of the subject from the data acquired in stepa), the image of the subject containing artifacts associated with thedata inconsistencies; c) forming an image matrix having a first columncorresponding to the image reconstructed in step b); d) computing atarget image matrix by iteratively updating the image matrix formed instep c) by minimizing a matrix rank of the image matrix subject to adata consistency condition such that each column of the computed targetimage matrix corresponds to a different one of the plurality of dataconsistency classes; and e) providing each column of the target imagematrix computed in step d) as an image of the subject that issubstantially free of artifacts to produce a series of images of thesubject at a first temporal resolution; f) deconvolving the series ofimages of the subject at the first temporal resolution using a finitetemporal window to generate a series of images of the subject withsecond temporal resolution that is higher than the first temporalresolution; and g) subtracting the series of images of the subject withthe second temporal resolution and from mask images of the subject togenerate a time-resolved CT angiogram of the subject.
 11. The method asrecited in claim 10 in which the short scan has a range of 200 degreesor less, including a fan angle.
 12. The method as recited in claim 10 inwhich the CT imaging system generates a cone beam and wherein the seriesof images of the subject with the second temporal resolution aretime-resolved cone beam CT images that define a continuous temporalsampling.
 13. The method as recited in claim 10 further comprisingperforming a gamma-variate fit to the series of images of the subjectwith the second temporal resolution to correct for potential temporaltruncation effects caused by the limited scan range.
 14. The method asrecited in claim 10 further comprising h) applying a cone-beam forwardprojection to the time-resolved CT angiogram to generate a virtual 2Dangiography image.
 15. The method as recited in claim 10 in which stepa) includes an acquisition with intravenous (IV) contrast and withoutcontrast.
 16. The method as recited in claim 10 in which the CT imagingsystem is a C-arm CT imaging system.
 17. The method as recited in claim10 in which the plurality of data consistency classes in the dataacquired in step a) include a data consistency class for data consistentwith a true image of the subject and a data consistency class for dataconsistent with at least one artifact.
 18. The method as recited inclaim 10 in which the plurality of data consistency classes in the dataacquired in step a) include data consistency classes corresponding todata consistent with different physical states of the subject.
 19. Themethod as recited in claim 10 in which the plurality of data consistencyclasses in the data acquired in step a) include data consistency classescorresponding to data consistent with different view angles of the datawas acquired in step a).
 20. A cone-beam computed tomography (CT) systemcomprising: an x-ray source and associated detectors configured toacquire imaging data from a subject over a range of view angles; acomputer system including a processor configured to: a) controloperation of the x-ray source and associated detectors to acquire datafrom a subject with the CT imaging system using a limited scan rangethat is less than 360 degrees; b) initialize an image matrix havingcolumns that each correspond to a different image; c) reconstruct atleast one image of the subject having a first temporal resolution fromthe data acquired in step a) by: i) minimizing a matrix rank of theimage matrix; ii) constraining the rank minimization of step c)i)subject to a consistency condition that promotes a forward projection ofeach column in the image matrix to be consistent with a different subsetof the acquired data, each subset of the acquired data containing datathat are consistent with each other while being inconsistent with datain other subsets of the acquired data; d) perform a temporaldeconvolution of the at least one image using a finite temporal windowto generate at least one image of the subject with a second temporalresolution that is greater than the first temporal resolution; and e)subtract the at least one image of the subject with the second temporalresolution and a mask image of the subject to generate a time-resolvedCT angiogram of the subject.